Title : ( EXPONENTIAL GROWTH OF SOLUTIONS FOR A VARIABLE-EXPONENT FOURTH-ORDER VISCOELASTIC EQUATION WITH NONLINEAR BOUNDARY FEEDBACK )
Authors: Mohammad Shahrouzi ,
Full TextAbstract
In this paper we study a variable-exponent fourth-order viscoelastic equation of the form |ut|ρ(x)utt + ∆[(a + b|∆u|m(x)−2)∆u] − Z0t g(t − s)∆2u(s)ds = |u|p(x)−2u, in a bounded domain of Rn. Under suitable conditions on variable exponents and initial data, we prove that the solutions will grow up as an exponential function with positive initial energy level. Our result improves and extends many earlier results in the literature such as the one by Mahdi and Hakem (Ser. Math. Inform. 2020, https://doi.org/10.22190/FUMI2003647M).
Keywords
, Variable exponents, viscoelastic equation, weak solution.
@article{paperid:1104635,
author = {Shahrouzi, Mohammad},
title = {EXPONENTIAL GROWTH OF SOLUTIONS FOR A VARIABLE-EXPONENT FOURTH-ORDER VISCOELASTIC EQUATION WITH NONLINEAR BOUNDARY FEEDBACK},
journal = {Facta Universitatis-Series: Mathematics and Informatics},
year = {2022},
month = {September},
issn = {0352-9665},
keywords = {Variable exponents; viscoelastic equation; weak solution.},
}
%0 Journal Article
%T EXPONENTIAL GROWTH OF SOLUTIONS FOR A VARIABLE-EXPONENT FOURTH-ORDER VISCOELASTIC EQUATION WITH NONLINEAR BOUNDARY FEEDBACK
%A Shahrouzi, Mohammad
%J Facta Universitatis-Series: Mathematics and Informatics
%@ 0352-9665
%D 2022
